Is there a module which can generate strings that satisfy a certain regular expression?

No.

That's a very hard question. For many types of grammars,
this question is known to be non-solvable. IIRC, this includes
regular expressions (the real ones, not the Perl ones).
Perl regular expressions are hard to categorize, but they
are certainly a superset of classical regular expressions.

This of course doesn't mean it's not possible for specific
regular expressions.

Warning: Theoretical but impractical stuff follows: I think for plain regular expressions (not the Perl stuff), it is possible to check whether a RE matches any string, and in the process of doing that, you (can) come across a lot of matching strings :

Any regular expression can be written as a finite deterministic automaton.

Every deterministic finite automaton (DFA) either accepts no word at all or at least one word that is equal or less the number of states it has.This theorem has some name I forgot...

If a DFA accepts a word of a length greater than the number of states, it has a loop.

If all of the above are true (and I remember them being true), then you "only" have to enumerate all strings from the alphabet from length 0 to the number of states of the DFA representing your RE. After that, you can go up to 2* number of states of DFA, to see whether it has loops.

The number of states in a DFA does not directly relate to the number of characters in your RE, if I remember correctly, it can be up to 2^n with n the number of characters from your alphabet in your RE (that's a rough number, as I equate the NFA with the RE here).

This means that, for nontrivial REs, you will have a large space of strings to search. It might be easier to randomly generate strings and check whether they match, maybe guided by some heuristics, like alphabetical chars within the RE.

For Perl regexes, its seems rosy until you reach
look-aheads. /^(?=$rx1)$rx2/ needs to find the
intersection between the two languages defined
but $rx1 and $rx2, if it exists. Without the ^
anchor $rx1 is floating in $rx2, it becomes
substring instead of intersection.